Optimal arguments in Jackson's inequality in the power-weighted space \(L_2(\mathbb R^d)\)

DOI10.1134/S0001434613090034zbMath1284.42070MaRDI QIDQ2436366

Valeriĭ I. Ivanov, Alexey Ivanov

Publication date: 24 February 2014

Published in: Mathematical Notes (Search for Journal in Brave)

zbMATH Keywords

modulus of continuityskew fieldHölder's inequalityJackson's inequalityDunkl transformLogan's problempower-weighted space \(L_2(\mathbb R^d)\)

Mathematics Subject Classification ID

Function spaces arising in harmonic analysis (42B35) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10)

Related Items (13)

Jackson-Stechkin Inequality and Values of Widths of Some Classes of Functions in $L_2$ ⋮ Generalized Logan's problem for entire functions of exponential type and optimal argument in Jackson's inequality in \(L_2(\mathbb{R}^3)\) ⋮ НЕКОТОРЫЕ ЭКСТРЕМАЛЬНЫЕ ЗАДАЧИ ГАРМОНИЧЕСКОГО АНАЛИЗА И ТЕОРИИ ПРИБЛИЖЕНИЙ ⋮ Вторая экстремальная задача Логана для преобразования Фурье по собственным функциям оператора Штурма–Лиувилля ⋮ Approximation in \(L_2\) by partial integrals of the Fourier transform over the eigenfunctions of the Sturm-Liouville operator ⋮ Approximation in \(L_2\) by partial integrals of the multidimensional Fourier transform over the eigenfunctions of the Sturm-Liouville operator ⋮ An estimate of an optimal argument in the sharp multidimensional Jackson-Stechkin \(L_2\)-inequality ⋮ Generalized Jackson inequality in the space \(L_2(\mathbb{R}^{d})\) with Dunkl weight ⋮ Multidimensional Extremal Logan’s and Bohman’s Problems ⋮ Approximation of the multidimensional Jacobi transform in \(L_2\) by partial integrals ⋮ A sharp Jackson inequality in \(L_p (\mathbb{R}^d)\) with Dunkl weight ⋮ Optimal arguments in the Jackson-Stechkin inequality in \(L_2(\mathbb R^d)\) with Dunkl weight ⋮ Optimal argument in the sharp Jackson inequality in the space \(L_2\) with hyperbolic weight

Cites Work

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• Multidimensional Jackson theorem in \(L_ 2\).
• Two related extremal problems for entire functions of several variables
• Extremal Problems for Positive-Definite Bandlimited Functions. I. Eventually Positive Functions with Zero Integral
• A Quadrature Formula Involving Zeros of Bessel Functions
• A Quadrature Formula with Zeros of Bessel Functions as Nodes
• Paley–Wiener theorems for the Dunkl transform
• Extremum problems for entire functions of exponential spherical type

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